Mission ATLAS #12 — Ghost Particle: The de Broglie Gate

MISSION ATLAS #12 · THE HELIOS INCIDENT — EPISODE 3 · MATTER WAVES

👻 GHOST PARTICLE: The de Broglie Gate

Derelict hull · docking clamp 3de Broglie 1924 · Davisson–Germer 1927ONE relationship: λ = h/p

🎯 Learning target

Master ONE relationship — the de Broglie wavelength of an electron:
λ = 1.227/√K (λ in nm, K in eV; K equals the gun voltage numerically)
Forward, inverse, and on an unknown leak.

⚠️ Misconception to break

"Electrons are tiny balls — waves need crowds." No: fired one at a time, each electron still builds an interference pattern. Every particle carries a wavelength.

🧪 Model & assumptions (stated honestly)

Non-relativistic electrons (error <0.5% up to 10 keV here) · teaching constant 1.227 nm·eV^½ (exact 1.2264) · K[eV] = gun voltage[V] numerically · the on-screen fringe pattern is qualitative (spacing ∝ λ, never graded) · single-electron buildup is real physics — Tonomura, 1989.

Difficulty generous tolerances

📐 Key formulas (given)

de Broglie: λ = h/p electron gun: λ = 1.227/√K [nm, eV] inverse: K = (1.227/λ)² K [eV] = V [volt] (numerically) perfect squares make √ friendly — the ship knows.

🚪 Curriculum — 4 hatches

1️⃣ Antechamber · Watch — one electron at a time, still a wave
2️⃣ Tune · Predict — V is given; your λ arms the gun
3️⃣ Cut the Key · Inverse — hatch wants λ; you set V
4️⃣ The Leak · Crisis — stray electrons, 90 s, name the live system
Bronze+ opens the next hatch. Scenarios re-roll every retry.

Controls

Space fire · Enter commit · P pause · R reset hatch · H hint. Each hatch opens with a 🧠 reasoning question. Wrong submissions −2 pts.

🏅 How scoring works

Every stage: answer the reasoning question, then compute and commit a number. Your medal is set by accuracy — 🥇 under 5% · 🥈 under 10% · 🥉 under 20% error — and a Bronze or better unlocks the next stage. A wrong answer costs −2 points (−1 on Easy, and your first reasoning slip on each question is free on Easy). A hint costs −3/−4/−5. Fewer tries and higher accuracy mean a higher score — so it always pays to calculate, not guess.